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The formula that blew up Wall Street

In 2000 a brilliant quant named David X. Li devised a mathematical formula called a copula function that got widely used by Wall Street to model risk.

Li came up with an ingenious way to model default correlation without even looking at historical default data. Instead, he used market data about the prices of instruments known as credit default swaps.

The problem was, even though Li and others warned repeatedly about this, the formula should never have been used to value, quite literally, trillions of dollars worth of bizarre hard-to-price CDSs and CDOs. Also, ahem, since CDS are not traded on open markets and are not regulated, seems to me it might be possible to play games with their pricing. Not that any traders would engage such unethical and probably illegal activities, of course.

And because the copula function used CDS prices to calculate correlation, it was forced to confine itself to looking at the period of time when those credit default swaps had been in existence: less than a decade, a period when house prices soared. Naturally, default correlations were very low in those years. But when the mortgage boom ended abruptly and home values started falling across the country, correlations soared.

The underlying assumption was housing prices would continue rising and most of those who used and abused the copula function never much cared if it was logical or even understood the model.

As Li himself said of his own model: “The most dangerous part is when people believe everything coming out of it.”